This comment is in response to a suggestion that another person may want to mock the speaker for some reason. It basically means: 'OK, mock me. I don't care!' 'Fine. Go ahead and mock me as much as you want to.' 'Feel free to mock me, then. I won't stop you.' This is the next chapter in your tutorial about adding little extra words to verbs. Remember how we demonstrated that 'up' added an idea of completeness to the verb a while ago? Well, adding 'away' can add the idea of freedom and lack of restraint or concern. For example: We were chatting away in the airport lounge, and we never noticed that our flight was being called.

Adding "away" in this sense means something like "as much as it pleases you" or "to your heart's content". It also means the speaker won't stop the other person from mocking.